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Completeness-Resolvable Graphs [PDF]
Graphs and Combinatorics, 2022 Given a connected graph $G=(V(G), E(G))$, the length of a shortest path from a vertex $u$ to a vertex $v$ is denoted by $d(u,v)$. For a proper subset $W$ of $V(G)$, let $m(W)$ be the maximum value of $d(u,v)$ as $u$ ranging over $W$ and $v$ ranging over $V(G)\setminus W$. The proper subset $W=\{w_1,\ldots,w_{|W|}\}$ is a {\em completeness-resolving set}
Min Feng 0004, Xuanlong Ma, Huiling Xu
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Some New Results on Lucky Labeling
مجلة بغداد للعلوم, 2023 Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if for every pair ...
J. Ashwini +2 more
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Dispersion on the Complete Graph
Random Structures & Algorithms, 2023 ABSTRACTWe consider a synchronous process of particles moving on the vertices of a graph , introduced by Cooper et al. Initially, particles are placed on a vertex of . At the beginning of each time step, for every vertex inhabited by at least two particles, each of these particles moves independently to a neighbor chosen uniformly at random.
Umberto De Ambroggio +2 more
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Uniform (Ck, Pk+1)-Factorizations of Kn − I When k Is Even
Mathematics, 2022 Let H be a connected subgraph of a graph G. An H-factor of G is a spanning subgraph of G whose components are isomorphic to H. Given a set H of mutually non-isomorphic graphs, a uniform H-factorization of G is a partition of the edges of G into H-factors
Giovanni Lo Faro +2 more
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Shannon Entropy of Ramsey Graphs with up to Six Vertices
Entropy, 2023 Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced and calculated for complete graphs containing up to six vertices. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links, are ...
Mark Frenkel +2 more
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Weak saturation numbers of and
AKCE International Journal of Graphs and Combinatorics, 2019 A graph is weakly -saturated if contains no copy of , and there is an ordering of all edges of so that if they are added one at a time, they form a complete graph and each edge added creates a new copy of .
Yajuan Cui, Liqun Pu
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On Topological Indices for Swapped Networks Modeled by Optical Transpose Interconnection System
IEEE Access, 2020 The optical transpose interconnection system (OTIS) network has many application in architecture for parallel as well as in distributed network. The optical translate interconnection system utilizes a straightforward pair of lenslet clusters to execute a
Nida Zahra +2 more
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Some Properties of the Members of Petersen Family
Tikrit Journal of Pure Science, 2023 This article has restudied the Petersen family in Graph Theory. It discussed the process of establishing this family. This discussion leads to discovering some new properties of the Petersen family's members.
Israa M. Tawfik
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Complete bipartite graph is a totally irregular total graph
Electronic Journal of Graph Theory and Applications, 2021 A graph G is called a totally irregular total k-graph if it has a totally irregular total k-labeling λ : V ∪ E→ 1, 2, ... , k, that is a total labeling such that for any pair of different vertices x and y of G, their weights wt(x) and wt(y) are distinct,
Meilin I. Tilukay +4 more
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Treewidth of the Line Graph of a Complete Graph [PDF]
Journal of Graph Theory, 2014 AbstractIn recent articles by Grohe and Marx, the treewidth of the line graph of a complete graph is a critical example—in a certain sense, every graph with large treewidth “contains” . However, the treewidth of was not determined exactly. We determine the exact treewidth of the line graph of a complete graph.
Daniel J. Harvey, David R. Wood
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